Properties

Label 108.4.h.b.35.5
Level 108
Weight 4
Character 108.35
Analytic conductor 6.372
Analytic rank 0
Dimension 24
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) \(=\) \( 108 = 2^{2} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 108.h (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.37220628062\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(12\) over \(\Q(\zeta_{6})\)
Twist minimal: no (minimal twist has level 36)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 35.5
Character \(\chi\) \(=\) 108.35
Dual form 108.4.h.b.71.5

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.823719 + 2.70582i) q^{2} +(-6.64298 - 4.45768i) q^{4} +(4.71466 - 2.72201i) q^{5} +(20.9358 + 12.0873i) q^{7} +(17.5336 - 14.3029i) q^{8} +O(q^{10})\) \(q+(-0.823719 + 2.70582i) q^{2} +(-6.64298 - 4.45768i) q^{4} +(4.71466 - 2.72201i) q^{5} +(20.9358 + 12.0873i) q^{7} +(17.5336 - 14.3029i) q^{8} +(3.48173 + 14.9992i) q^{10} +(-25.3999 + 43.9939i) q^{11} +(25.0883 + 43.4542i) q^{13} +(-49.9512 + 46.6920i) q^{14} +(24.2582 + 59.2245i) q^{16} -51.7146i q^{17} +27.9305i q^{19} +(-43.4533 - 2.93419i) q^{20} +(-98.1174 - 104.966i) q^{22} +(3.93548 + 6.81645i) q^{23} +(-47.6813 + 82.5864i) q^{25} +(-138.245 + 32.0905i) q^{26} +(-85.1946 - 173.620i) q^{28} +(212.788 + 122.853i) q^{29} +(-51.4009 + 29.6763i) q^{31} +(-180.233 + 16.8542i) q^{32} +(139.931 + 42.5982i) q^{34} +131.607 q^{35} +295.334 q^{37} +(-75.5750 - 23.0069i) q^{38} +(43.7327 - 115.160i) q^{40} +(146.833 - 84.7741i) q^{41} +(-284.968 - 164.526i) q^{43} +(364.841 - 179.026i) q^{44} +(-21.6859 + 5.03388i) q^{46} +(47.9742 - 83.0938i) q^{47} +(120.704 + 209.066i) q^{49} +(-184.188 - 197.045i) q^{50} +(27.0439 - 400.500i) q^{52} -300.751i q^{53} +276.555i q^{55} +(539.963 - 87.5075i) q^{56} +(-507.697 + 474.571i) q^{58} +(-113.273 - 196.195i) q^{59} +(173.722 - 300.896i) q^{61} +(-37.9590 - 163.527i) q^{62} +(102.857 - 501.562i) q^{64} +(236.566 + 136.581i) q^{65} +(904.675 - 522.314i) q^{67} +(-230.527 + 343.538i) q^{68} +(-108.407 + 356.105i) q^{70} -243.524 q^{71} -1094.68 q^{73} +(-243.272 + 799.122i) q^{74} +(124.505 - 185.542i) q^{76} +(-1063.53 + 614.031i) q^{77} +(-530.679 - 306.388i) q^{79} +(275.579 + 213.192i) q^{80} +(108.435 + 467.135i) q^{82} +(-283.063 + 490.280i) q^{83} +(-140.768 - 243.817i) q^{85} +(679.912 - 635.549i) q^{86} +(183.886 + 1134.66i) q^{88} +212.529i q^{89} +1213.00i q^{91} +(4.24224 - 62.8246i) q^{92} +(185.320 + 198.256i) q^{94} +(76.0272 + 131.683i) q^{95} +(234.298 - 405.817i) q^{97} +(-665.122 + 154.393i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q - 12q^{4} + 72q^{5} + O(q^{10}) \) \( 24q - 12q^{4} + 72q^{5} + 96q^{10} - 216q^{13} + 36q^{14} - 72q^{16} + 540q^{20} - 192q^{22} + 252q^{25} - 672q^{28} - 576q^{29} - 360q^{32} - 660q^{34} + 1248q^{37} + 144q^{38} + 636q^{40} - 1116q^{41} + 960q^{46} + 348q^{49} + 648q^{50} + 132q^{52} + 1692q^{56} + 516q^{58} - 264q^{61} + 960q^{64} + 2592q^{65} - 5688q^{68} + 564q^{70} - 4776q^{73} - 5652q^{74} - 600q^{76} - 648q^{77} - 4104q^{82} + 720q^{85} + 9540q^{86} + 1956q^{88} + 7416q^{92} - 1188q^{94} + 588q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/108\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(55\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(-1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.823719 + 2.70582i −0.291229 + 0.956654i
\(3\) 0 0
\(4\) −6.64298 4.45768i −0.830372 0.557210i
\(5\) 4.71466 2.72201i 0.421692 0.243464i −0.274109 0.961699i \(-0.588383\pi\)
0.695801 + 0.718234i \(0.255049\pi\)
\(6\) 0 0
\(7\) 20.9358 + 12.0873i 1.13043 + 0.652651i 0.944042 0.329826i \(-0.106990\pi\)
0.186383 + 0.982477i \(0.440323\pi\)
\(8\) 17.5336 14.3029i 0.774885 0.632103i
\(9\) 0 0
\(10\) 3.48173 + 14.9992i 0.110102 + 0.474317i
\(11\) −25.3999 + 43.9939i −0.696214 + 1.20588i 0.273556 + 0.961856i \(0.411800\pi\)
−0.969770 + 0.244022i \(0.921533\pi\)
\(12\) 0 0
\(13\) 25.0883 + 43.4542i 0.535249 + 0.927078i 0.999151 + 0.0411921i \(0.0131156\pi\)
−0.463902 + 0.885886i \(0.653551\pi\)
\(14\) −49.9512 + 46.6920i −0.953573 + 0.891355i
\(15\) 0 0
\(16\) 24.2582 + 59.2245i 0.379035 + 0.925382i
\(17\) 51.7146i 0.737801i −0.929469 0.368901i \(-0.879734\pi\)
0.929469 0.368901i \(-0.120266\pi\)
\(18\) 0 0
\(19\) 27.9305i 0.337247i 0.985681 + 0.168624i \(0.0539322\pi\)
−0.985681 + 0.168624i \(0.946068\pi\)
\(20\) −43.4533 2.93419i −0.485822 0.0328052i
\(21\) 0 0
\(22\) −98.1174 104.966i −0.950850 1.01722i
\(23\) 3.93548 + 6.81645i 0.0356785 + 0.0617969i 0.883313 0.468783i \(-0.155307\pi\)
−0.847635 + 0.530580i \(0.821974\pi\)
\(24\) 0 0
\(25\) −47.6813 + 82.5864i −0.381450 + 0.660691i
\(26\) −138.245 + 32.0905i −1.04277 + 0.242056i
\(27\) 0 0
\(28\) −85.1946 173.620i −0.575010 1.17183i
\(29\) 212.788 + 122.853i 1.36254 + 0.786665i 0.989962 0.141335i \(-0.0451395\pi\)
0.372581 + 0.928000i \(0.378473\pi\)
\(30\) 0 0
\(31\) −51.4009 + 29.6763i −0.297802 + 0.171936i −0.641455 0.767161i \(-0.721669\pi\)
0.343653 + 0.939097i \(0.388336\pi\)
\(32\) −180.233 + 16.8542i −0.995656 + 0.0931073i
\(33\) 0 0
\(34\) 139.931 + 42.5982i 0.705820 + 0.214869i
\(35\) 131.607 0.635589
\(36\) 0 0
\(37\) 295.334 1.31223 0.656116 0.754660i \(-0.272198\pi\)
0.656116 + 0.754660i \(0.272198\pi\)
\(38\) −75.5750 23.0069i −0.322629 0.0982160i
\(39\) 0 0
\(40\) 43.7327 115.160i 0.172868 0.455210i
\(41\) 146.833 84.7741i 0.559304 0.322915i −0.193562 0.981088i \(-0.562004\pi\)
0.752866 + 0.658173i \(0.228671\pi\)
\(42\) 0 0
\(43\) −284.968 164.526i −1.01063 0.583488i −0.0992550 0.995062i \(-0.531646\pi\)
−0.911376 + 0.411574i \(0.864979\pi\)
\(44\) 364.841 179.026i 1.25004 0.613390i
\(45\) 0 0
\(46\) −21.6859 + 5.03388i −0.0695088 + 0.0161349i
\(47\) 47.9742 83.0938i 0.148888 0.257882i −0.781928 0.623368i \(-0.785764\pi\)
0.930817 + 0.365486i \(0.119097\pi\)
\(48\) 0 0
\(49\) 120.704 + 209.066i 0.351908 + 0.609522i
\(50\) −184.188 197.045i −0.520964 0.557328i
\(51\) 0 0
\(52\) 27.0439 400.500i 0.0721213 1.06807i
\(53\) 300.751i 0.779459i −0.920929 0.389729i \(-0.872569\pi\)
0.920929 0.389729i \(-0.127431\pi\)
\(54\) 0 0
\(55\) 276.555i 0.678013i
\(56\) 539.963 87.5075i 1.28849 0.208816i
\(57\) 0 0
\(58\) −507.697 + 474.571i −1.14938 + 1.07438i
\(59\) −113.273 196.195i −0.249947 0.432921i 0.713564 0.700590i \(-0.247080\pi\)
−0.963511 + 0.267669i \(0.913747\pi\)
\(60\) 0 0
\(61\) 173.722 300.896i 0.364637 0.631570i −0.624081 0.781360i \(-0.714526\pi\)
0.988718 + 0.149790i \(0.0478597\pi\)
\(62\) −37.9590 163.527i −0.0777548 0.334966i
\(63\) 0 0
\(64\) 102.857 501.562i 0.200892 0.979613i
\(65\) 236.566 + 136.581i 0.451421 + 0.260628i
\(66\) 0 0
\(67\) 904.675 522.314i 1.64961 0.952401i 0.672378 0.740208i \(-0.265273\pi\)
0.977228 0.212193i \(-0.0680605\pi\)
\(68\) −230.527 + 343.538i −0.411110 + 0.612649i
\(69\) 0 0
\(70\) −108.407 + 356.105i −0.185102 + 0.608038i
\(71\) −243.524 −0.407057 −0.203528 0.979069i \(-0.565241\pi\)
−0.203528 + 0.979069i \(0.565241\pi\)
\(72\) 0 0
\(73\) −1094.68 −1.75510 −0.877552 0.479481i \(-0.840825\pi\)
−0.877552 + 0.479481i \(0.840825\pi\)
\(74\) −243.272 + 799.122i −0.382159 + 1.25535i
\(75\) 0 0
\(76\) 124.505 185.542i 0.187917 0.280041i
\(77\) −1063.53 + 614.031i −1.57404 + 0.908770i
\(78\) 0 0
\(79\) −530.679 306.388i −0.755773 0.436346i 0.0720031 0.997404i \(-0.477061\pi\)
−0.827776 + 0.561059i \(0.810394\pi\)
\(80\) 275.579 + 213.192i 0.385134 + 0.297945i
\(81\) 0 0
\(82\) 108.435 + 467.135i 0.146032 + 0.629103i
\(83\) −283.063 + 490.280i −0.374340 + 0.648376i −0.990228 0.139458i \(-0.955464\pi\)
0.615888 + 0.787834i \(0.288797\pi\)
\(84\) 0 0
\(85\) −140.768 243.817i −0.179628 0.311125i
\(86\) 679.912 635.549i 0.852521 0.796896i
\(87\) 0 0
\(88\) 183.886 + 1134.66i 0.222754 + 1.37450i
\(89\) 212.529i 0.253124i 0.991959 + 0.126562i \(0.0403943\pi\)
−0.991959 + 0.126562i \(0.959606\pi\)
\(90\) 0 0
\(91\) 1213.00i 1.39732i
\(92\) 4.24224 62.8246i 0.00480744 0.0711948i
\(93\) 0 0
\(94\) 185.320 + 198.256i 0.203343 + 0.217537i
\(95\) 76.0272 + 131.683i 0.0821076 + 0.142215i
\(96\) 0 0
\(97\) 234.298 405.817i 0.245252 0.424788i −0.716951 0.697124i \(-0.754463\pi\)
0.962202 + 0.272336i \(0.0877961\pi\)
\(98\) −665.122 + 154.393i −0.685587 + 0.159143i
\(99\) 0 0
\(100\) 684.889 336.072i 0.684889 0.336072i
\(101\) −1552.98 896.613i −1.52997 0.883330i −0.999362 0.0357140i \(-0.988629\pi\)
−0.530610 0.847616i \(-0.678037\pi\)
\(102\) 0 0
\(103\) 119.871 69.2074i 0.114672 0.0662059i −0.441567 0.897228i \(-0.645577\pi\)
0.556239 + 0.831022i \(0.312244\pi\)
\(104\) 1061.41 + 403.076i 1.00077 + 0.380046i
\(105\) 0 0
\(106\) 813.779 + 247.734i 0.745672 + 0.227001i
\(107\) 771.292 0.696857 0.348428 0.937335i \(-0.386715\pi\)
0.348428 + 0.937335i \(0.386715\pi\)
\(108\) 0 0
\(109\) −275.772 −0.242332 −0.121166 0.992632i \(-0.538663\pi\)
−0.121166 + 0.992632i \(0.538663\pi\)
\(110\) −748.310 227.804i −0.648623 0.197457i
\(111\) 0 0
\(112\) −207.998 + 1533.13i −0.175481 + 1.29345i
\(113\) 542.916 313.453i 0.451976 0.260948i −0.256689 0.966494i \(-0.582631\pi\)
0.708664 + 0.705546i \(0.249298\pi\)
\(114\) 0 0
\(115\) 37.1089 + 21.4249i 0.0300907 + 0.0173729i
\(116\) −865.906 1764.65i −0.693080 1.41245i
\(117\) 0 0
\(118\) 624.173 144.888i 0.486947 0.113034i
\(119\) 625.088 1082.68i 0.481527 0.834029i
\(120\) 0 0
\(121\) −624.809 1082.20i −0.469428 0.813073i
\(122\) 671.073 + 717.916i 0.498001 + 0.532762i
\(123\) 0 0
\(124\) 473.742 + 31.9895i 0.343091 + 0.0231673i
\(125\) 1199.66i 0.858406i
\(126\) 0 0
\(127\) 71.3408i 0.0498463i 0.999689 + 0.0249231i \(0.00793410\pi\)
−0.999689 + 0.0249231i \(0.992066\pi\)
\(128\) 1272.41 + 691.458i 0.878645 + 0.477475i
\(129\) 0 0
\(130\) −564.428 + 527.601i −0.380797 + 0.355951i
\(131\) 358.903 + 621.638i 0.239370 + 0.414601i 0.960534 0.278164i \(-0.0897258\pi\)
−0.721164 + 0.692765i \(0.756392\pi\)
\(132\) 0 0
\(133\) −337.604 + 584.747i −0.220105 + 0.381233i
\(134\) 668.093 + 2878.13i 0.430705 + 1.85547i
\(135\) 0 0
\(136\) −739.666 906.744i −0.466366 0.571711i
\(137\) −190.925 110.231i −0.119065 0.0687420i 0.439285 0.898348i \(-0.355232\pi\)
−0.558350 + 0.829606i \(0.688565\pi\)
\(138\) 0 0
\(139\) 1214.70 701.309i 0.741222 0.427945i −0.0812916 0.996690i \(-0.525905\pi\)
0.822513 + 0.568746i \(0.192571\pi\)
\(140\) −874.261 586.661i −0.527775 0.354156i
\(141\) 0 0
\(142\) 200.596 658.934i 0.118547 0.389412i
\(143\) −2548.96 −1.49059
\(144\) 0 0
\(145\) 1337.63 0.766099
\(146\) 901.708 2962.01i 0.511136 1.67903i
\(147\) 0 0
\(148\) −1961.90 1316.50i −1.08964 0.731188i
\(149\) 1289.36 744.413i 0.708917 0.409293i −0.101743 0.994811i \(-0.532442\pi\)
0.810660 + 0.585517i \(0.199109\pi\)
\(150\) 0 0
\(151\) −1704.17 983.903i −0.918433 0.530257i −0.0352979 0.999377i \(-0.511238\pi\)
−0.883135 + 0.469120i \(0.844571\pi\)
\(152\) 399.486 + 489.723i 0.213175 + 0.261328i
\(153\) 0 0
\(154\) −785.408 3383.52i −0.410974 1.77047i
\(155\) −161.559 + 279.828i −0.0837206 + 0.145008i
\(156\) 0 0
\(157\) 564.122 + 977.088i 0.286763 + 0.496689i 0.973035 0.230656i \(-0.0740874\pi\)
−0.686272 + 0.727345i \(0.740754\pi\)
\(158\) 1266.16 1183.55i 0.637534 0.595937i
\(159\) 0 0
\(160\) −803.861 + 570.059i −0.397192 + 0.281669i
\(161\) 190.277i 0.0931424i
\(162\) 0 0
\(163\) 1940.05i 0.932250i −0.884719 0.466125i \(-0.845650\pi\)
0.884719 0.466125i \(-0.154350\pi\)
\(164\) −1353.30 91.3821i −0.644362 0.0435106i
\(165\) 0 0
\(166\) −1093.45 1169.77i −0.511252 0.546939i
\(167\) −1242.52 2152.11i −0.575743 0.997217i −0.995960 0.0897933i \(-0.971379\pi\)
0.420217 0.907424i \(1.63805\pi\)
\(168\) 0 0
\(169\) −160.344 + 277.723i −0.0729830 + 0.126410i
\(170\) 775.678 180.056i 0.349952 0.0812334i
\(171\) 0 0
\(172\) 1159.63 + 2363.24i 0.514075 + 1.04765i
\(173\) 2492.67 + 1439.15i 1.09546 + 0.632464i 0.935025 0.354583i \(-0.115377\pi\)
0.160435 + 0.987046i \(0.448710\pi\)
\(174\) 0 0
\(175\) −1996.49 + 1152.67i −0.862402 + 0.497908i
\(176\) −3221.67 437.081i −1.37979 0.187194i
\(177\) 0 0
\(178\) −575.067 175.064i −0.242152 0.0737170i
\(179\) 2965.78 1.23840 0.619198 0.785235i \(-0.287458\pi\)
0.619198 + 0.785235i \(0.287458\pi\)
\(180\) 0 0
\(181\) 1250.55 0.513551 0.256776 0.966471i \(-0.417340\pi\)
0.256776 + 0.966471i \(0.417340\pi\)
\(182\) −3282.15 999.167i −1.33675 0.406941i
\(183\) 0 0
\(184\) 166.498 + 63.2286i 0.0667087 + 0.0253330i
\(185\) 1392.40 803.902i 0.553358 0.319482i
\(186\) 0 0
\(187\) 2275.12 + 1313.54i 0.889698 + 0.513668i
\(188\) −689.097 + 338.136i −0.267327 + 0.131176i
\(189\) 0 0
\(190\) −418.936 + 97.2465i −0.159962 + 0.0371316i
\(191\) 387.763 671.626i 0.146898 0.254435i −0.783181 0.621793i \(-0.786404\pi\)
0.930080 + 0.367358i \(0.119738\pi\)
\(192\) 0 0
\(193\) 2185.71 + 3785.76i 0.815185 + 1.41194i 0.909195 + 0.416370i \(0.136698\pi\)
−0.0940101 + 0.995571i \(0.529969\pi\)
\(194\) 905.073 + 968.249i 0.334951 + 0.358331i
\(195\) 0 0
\(196\) 130.113 1926.88i 0.0474173 0.702216i
\(197\) 1648.60i 0.596233i −0.954530 0.298116i \(-0.903642\pi\)
0.954530 0.298116i \(-0.0963584\pi\)
\(198\) 0 0
\(199\) 2946.42i 1.04958i 0.851232 + 0.524790i \(0.175856\pi\)
−0.851232 + 0.524790i \(0.824144\pi\)
\(200\) 345.195 + 2130.02i 0.122045 + 0.753075i
\(201\) 0 0
\(202\) 3705.30 3463.53i 1.29061 1.20640i
\(203\) 2969.92 + 5144.05i 1.02684 + 1.77853i
\(204\) 0 0
\(205\) 461.513 799.363i 0.157236 0.272341i
\(206\) 88.5233 + 381.356i 0.0299403 + 0.128982i
\(207\) 0 0
\(208\) −1964.95 + 2539.96i −0.655024 + 0.846705i
\(209\) −1228.77 709.432i −0.406679 0.234796i
\(210\) 0 0
\(211\) −477.089 + 275.447i −0.155659 + 0.0898700i −0.575806 0.817586i \(-0.695312\pi\)
0.420147 + 0.907456i \(0.361979\pi\)
\(212\) −1340.65 + 1997.88i −0.434322 + 0.647241i
\(213\) 0 0
\(214\) −635.328 + 2086.98i −0.202945 + 0.666650i
\(215\) −1791.37 −0.568234
\(216\) 0 0
\(217\) −1434.82 −0.448857
\(218\) 227.159 746.192i 0.0705741 0.231828i
\(219\) 0 0
\(220\) 1232.79 1837.15i 0.377795 0.563003i
\(221\) 2247.21 1297.43i 0.684000 0.394907i
\(222\) 0 0
\(223\) −1564.82 903.449i −0.469902 0.271298i 0.246297 0.969194i \(-0.420786\pi\)
−0.716199 + 0.697897i \(0.754120\pi\)
\(224\) −3977.04 1825.67i −1.18628 0.544565i
\(225\) 0 0
\(226\) 400.938 + 1727.23i 0.118009 + 0.508380i
\(227\) −752.796 + 1303.88i −0.220109 + 0.381241i −0.954841 0.297117i \(-0.903975\pi\)
0.734732 + 0.678358i \(0.237308\pi\)
\(228\) 0 0
\(229\) −767.015 1328.51i −0.221335 0.383364i 0.733878 0.679281i \(-0.237708\pi\)
−0.955214 + 0.295917i \(0.904375\pi\)
\(230\) −88.5392 + 82.7622i −0.0253831 + 0.0237269i
\(231\) 0 0
\(232\) 5488.10 889.413i 1.55307 0.251693i
\(233\) 1257.04i 0.353440i 0.984261 + 0.176720i \(0.0565487\pi\)
−0.984261 + 0.176720i \(0.943451\pi\)
\(234\) 0 0
\(235\) 522.346i 0.144996i
\(236\) −122.102 + 1808.25i −0.0336787 + 0.498759i
\(237\) 0 0
\(238\) 2414.66 + 2583.21i 0.657643 + 0.703548i
\(239\) −916.982 1588.26i −0.248178 0.429858i 0.714842 0.699286i \(-0.246499\pi\)
−0.963020 + 0.269428i \(0.913165\pi\)
\(240\) 0 0
\(241\) −358.771 + 621.410i −0.0958941 + 0.166094i −0.909981 0.414649i \(-0.863904\pi\)
0.814087 + 0.580743i \(0.197238\pi\)
\(242\) 3442.91 799.194i 0.914540 0.212290i
\(243\) 0 0
\(244\) −2495.33 + 1224.45i −0.654701 + 0.321259i
\(245\) 1138.16 + 657.117i 0.296794 + 0.171354i
\(246\) 0 0
\(247\) −1213.70 + 700.728i −0.312655 + 0.180511i
\(248\) −476.788 + 1255.51i −0.122081 + 0.321472i
\(249\) 0 0
\(250\) −3246.07 988.182i −0.821198 0.249992i
\(251\) −1053.84 −0.265010 −0.132505 0.991182i \(-0.542302\pi\)
−0.132505 + 0.991182i \(0.542302\pi\)
\(252\) 0 0
\(253\) −399.843 −0.0993594
\(254\) −193.036 58.7648i −0.0476856 0.0145167i
\(255\) 0 0
\(256\) −2919.08 + 2873.36i −0.712665 + 0.701504i
\(257\) −5985.55 + 3455.76i −1.45280 + 0.838772i −0.998639 0.0521496i \(-0.983393\pi\)
−0.454157 + 0.890922i \(0.650059\pi\)
\(258\) 0 0
\(259\) 6183.04 + 3569.78i 1.48338 + 0.856430i
\(260\) −962.665 1961.84i −0.229623 0.467954i
\(261\) 0 0
\(262\) −1977.68 + 459.073i −0.466341 + 0.108251i
\(263\) −1325.23 + 2295.36i −0.310712 + 0.538168i −0.978517 0.206168i \(-0.933901\pi\)
0.667805 + 0.744336i \(0.267234\pi\)
\(264\) 0 0
\(265\) −818.648 1417.94i −0.189770 0.328692i
\(266\) −1304.13 1395.16i −0.300607 0.321590i
\(267\) 0 0
\(268\) −8338.04 563.027i −1.90047 0.128330i
\(269\) 2386.16i 0.540843i −0.962742 0.270422i \(-0.912837\pi\)
0.962742 0.270422i \(-0.0871631\pi\)
\(270\) 0 0
\(271\) 4287.45i 0.961048i −0.876982 0.480524i \(-0.840446\pi\)
0.876982 0.480524i \(-0.159554\pi\)
\(272\) 3062.77 1254.50i 0.682748 0.279652i
\(273\) 0 0
\(274\) 455.534 425.811i 0.100437 0.0938839i
\(275\) −2422.20 4195.37i −0.531142 0.919965i
\(276\) 0 0
\(277\) −2416.58 + 4185.64i −0.524181 + 0.907909i 0.475422 + 0.879758i \(0.342295\pi\)
−0.999604 + 0.0281511i \(0.991038\pi\)
\(278\) 897.046 + 3864.46i 0.193530 + 0.833722i
\(279\) 0 0
\(280\) 2307.55 1882.35i 0.492508 0.401758i
\(281\) −1501.29 866.770i −0.318717 0.184011i 0.332104 0.943243i \(-0.392242\pi\)
−0.650821 + 0.759232i \(0.725575\pi\)
\(282\) 0 0
\(283\) 3227.63 1863.47i 0.677960 0.391420i −0.121126 0.992637i \(-0.538650\pi\)
0.799086 + 0.601217i \(0.205317\pi\)
\(284\) 1617.73 + 1085.55i 0.338009 + 0.226816i
\(285\) 0 0
\(286\) 2099.62 6897.03i 0.434103 1.42598i
\(287\) 4098.75 0.843003
\(288\) 0 0
\(289\) 2238.61 0.455649
\(290\) −1101.83 + 3619.40i −0.223110 + 0.732891i
\(291\) 0 0
\(292\) 7271.93 + 4879.73i 1.45739 + 0.977961i
\(293\) −5604.61 + 3235.82i −1.11749 + 0.645183i −0.940759 0.339076i \(-0.889886\pi\)
−0.176731 + 0.984259i \(0.556552\pi\)
\(294\) 0 0
\(295\) −1068.09 616.661i −0.210802 0.121706i
\(296\) 5178.28 4224.12i 1.01683 0.829466i
\(297\) 0 0
\(298\) 952.180 + 4101.97i 0.185095 + 0.797386i
\(299\) −197.469 + 342.026i −0.0381937 + 0.0661534i
\(300\) 0 0
\(301\) −3977.34 6888.96i −0.761629 1.31918i
\(302\) 4066.02 3800.72i 0.774746 0.724196i
\(303\) 0 0
\(304\) −1654.17 + 677.545i −0.312083 + 0.127828i
\(305\) 1891.50i 0.355104i
\(306\) 0 0
\(307\) 7858.86i 1.46101i −0.682909 0.730503i \(-0.739285\pi\)
0.682909 0.730503i \(-0.260715\pi\)
\(308\) 9802.17 + 661.893i 1.81341 + 0.122451i
\(309\) 0 0
\(310\) −624.086 667.648i −0.114341 0.122322i
\(311\) −3745.08 6486.66i −0.682842 1.18272i −0.974110 0.226075i \(-0.927410\pi\)
0.291268 0.956642i \(1.59408\pi\)
\(312\) 0 0
\(313\) 4304.38 7455.41i 0.777310 1.34634i −0.156176 0.987729i \(-0.549917\pi\)
0.933487 0.358612i \(-0.116750\pi\)
\(314\) −3108.51 + 721.570i −0.558672 + 0.129683i
\(315\) 0 0
\(316\) 2159.51 + 4400.92i 0.384437 + 0.783453i
\(317\) 4705.42 + 2716.67i 0.833699 + 0.481336i 0.855117 0.518434i \(-0.173485\pi\)
−0.0214185 + 0.999771i \(0.506818\pi\)
\(318\) 0 0
\(319\) −10809.6 + 6240.92i −1.89724 + 1.09537i
\(320\) −880.323 2644.67i −0.153786 0.462006i
\(321\) 0 0
\(322\) −514.856 156.735i −0.0891050 0.0271257i
\(323\) 1444.41 0.248821
\(324\) 0 0
\(325\) −4784.97 −0.816684
\(326\) 5249.44 + 1598.06i 0.891840 + 0.271498i
\(327\) 0 0
\(328\) 1362.01 3586.53i 0.229281 0.603759i
\(329\) 2008.75 1159.75i 0.336615 0.194344i
\(330\) 0 0
\(331\) 1367.21 + 789.359i 0.227035 + 0.131079i 0.609204 0.793014i \(-0.291489\pi\)
−0.382168 + 0.924093i \(0.624823\pi\)
\(332\) 4065.89 1995.11i 0.672122 0.329807i
\(333\) 0 0
\(334\) 6846.72 1589.31i 1.12166 0.260369i
\(335\) 2843.49 4925.07i 0.463751 0.803240i
\(336\) 0 0
\(337\) −3400.38 5889.62i −0.549645 0.952013i −0.998299 0.0583070i \(-0.981430\pi\)
0.448654 0.893706i \(-0.351904\pi\)
\(338\) −619.393 662.628i −0.0996761 0.106634i
\(339\) 0 0
\(340\) −151.740 + 2247.17i −0.0242037 + 0.358440i
\(341\) 3015.10i 0.478818i
\(342\) 0 0
\(343\) 2455.93i 0.386611i
\(344\) −7349.71 + 1191.11i −1.15195 + 0.186687i
\(345\) 0 0
\(346\) −5947.34 + 5559.29i −0.924078 + 0.863784i
\(347\) 6228.10 + 10787.4i 0.963522 + 1.66887i 0.713535 + 0.700620i \(0.247093\pi\)
0.249987 + 0.968249i \(0.419573\pi\)
\(348\) 0 0
\(349\) −910.729 + 1577.43i −0.139685 + 0.241942i −0.927378 0.374127i \(-0.877942\pi\)
0.787692 + 0.616069i \(0.211276\pi\)
\(350\) −1474.39 6351.63i −0.225169 0.970025i
\(351\) 0 0
\(352\) 3836.42 8357.25i 0.580914 1.26546i
\(353\) −6019.52 3475.37i −0.907611 0.524010i −0.0279495 0.999609i \(-0.508898\pi\)
−0.879662 + 0.475600i \(0.842231\pi\)
\(354\) 0 0
\(355\) −1148.14 + 662.877i −0.171653 + 0.0991038i
\(356\) 947.387 1411.83i 0.141043 0.210187i
\(357\) 0 0
\(358\) −2442.97 + 8024.88i −0.360656 + 1.18472i
\(359\) 318.743 0.0468597 0.0234298 0.999725i \(-0.492541\pi\)
0.0234298 + 0.999725i \(0.492541\pi\)
\(360\) 0 0
\(361\) 6078.89 0.886264
\(362\) −1030.10 + 3383.77i −0.149561 + 0.491290i
\(363\) 0 0
\(364\) 5407.14 8057.90i 0.778602 1.16030i
\(365\) −5161.05 + 2979.73i −0.740114 + 0.427305i
\(366\) 0 0
\(367\) 5425.21 + 3132.25i 0.771645 + 0.445510i 0.833461 0.552578i \(-0.186356\pi\)
−0.0618160 + 0.998088i \(0.519689\pi\)
\(368\) −308.233 + 398.432i −0.0436624 + 0.0564394i
\(369\) 0 0
\(370\) 1028.27 + 4429.78i 0.144479 + 0.622414i
\(371\) 3635.26 6296.45i 0.508715 0.881120i
\(372\) 0 0
\(373\) 6066.19 + 10506.9i 0.842078 + 1.45852i 0.888135 + 0.459583i \(0.152001\pi\)
−0.0460564 + 0.998939i \(0.514665\pi\)
\(374\) −5428.28 + 5074.10i −0.750508 + 0.701538i
\(375\) 0 0
\(376\) −347.316 2143.10i −0.0476368 0.293942i
\(377\) 12328.7i 1.68425i
\(378\) 0 0
\(379\) 1928.72i 0.261402i 0.991422 + 0.130701i \(0.0417229\pi\)
−0.991422 + 0.130701i \(0.958277\pi\)
\(380\) 81.9533 1213.67i 0.0110635 0.163842i
\(381\) 0 0
\(382\) 1497.89 + 1602.45i 0.200625 + 0.214630i
\(383\) −2974.93 5152.73i −0.396898 0.687448i 0.596443 0.802655i \(-0.296580\pi\)
−0.993341 + 0.115208i \(0.963247\pi\)
\(384\) 0 0
\(385\) −3342.80 + 5789.90i −0.442506 + 0.766443i
\(386\) −12044.0 + 2795.74i −1.58814 + 0.368652i
\(387\) 0 0
\(388\) −3365.44 + 1651.40i −0.440346 + 0.216076i
\(389\) −2023.11 1168.05i −0.263691 0.152242i 0.362326 0.932051i \(-0.381983\pi\)
−0.626017 + 0.779809i \(0.715316\pi\)
\(390\) 0 0
\(391\) 352.510 203.522i 0.0455938 0.0263236i
\(392\) 5106.63 + 1939.27i 0.657968 + 0.249867i
\(393\) 0 0
\(394\) 4460.82 + 1357.98i 0.570388 + 0.173640i
\(395\) −3335.97 −0.424938
\(396\) 0 0
\(397\) −6080.16 −0.768652 −0.384326 0.923198i \(-0.625566\pi\)
−0.384326 + 0.923198i \(0.625566\pi\)
\(398\) −7972.51 2427.02i −1.00408 0.305668i
\(399\) 0 0
\(400\) −6047.80 820.499i −0.755975 0.102562i
\(401\) 11997.7 6926.90i 1.49411 0.862626i 0.494135 0.869385i \(-0.335485\pi\)
0.999977 + 0.00675957i \(0.00215165\pi\)
\(402\) 0 0
\(403\) −2579.12 1489.05i −0.318797 0.184057i
\(404\) 6319.59 + 12878.9i 0.778246 + 1.58601i
\(405\) 0 0
\(406\) −16365.3 + 3798.83i −2.00048 + 0.464367i
\(407\) −7501.45 + 12992.9i −0.913594 + 1.58239i
\(408\) 0 0
\(409\) 135.435 + 234.581i 0.0163737 + 0.0283601i 0.874096 0.485753i \(-0.161455\pi\)
−0.857722 + 0.514113i \(0.828121\pi\)
\(410\) 1782.78 + 1907.22i 0.214745 + 0.229734i
\(411\) 0 0
\(412\) −1104.80 74.6019i −0.132111 0.00892081i
\(413\) 5476.64i 0.652513i
\(414\) 0 0
\(415\) 3082.01i 0.364553i
\(416\) −5254.12 7409.03i −0.619242 0.873216i
\(417\) 0 0
\(418\) 2931.76 2740.47i 0.343055 0.320672i
\(419\) 3950.75 + 6842.90i 0.460637 + 0.797846i 0.998993 0.0448712i \(-0.0142877\pi\)
−0.538356 + 0.842718i \(0.680954\pi\)
\(420\) 0 0
\(421\) 3331.91 5771.04i 0.385718 0.668083i −0.606150 0.795350i \(-0.707287\pi\)
0.991869 + 0.127267i \(0.0406204\pi\)
\(422\) −352.325 1517.81i −0.0406420 0.175085i
\(423\) 0 0
\(424\) −4301.60 5273.26i −0.492698 0.603991i
\(425\) 4270.92 + 2465.82i 0.487459 + 0.281435i
\(426\) 0 0
\(427\) 7274.02 4199.66i 0.824390 0.475962i
\(428\) −5123.68 3438.17i −0.578650 0.388295i
\(429\) 0 0
\(430\) 1475.58 4847.13i 0.165486 0.543603i
\(431\) −14773.0 −1.65102 −0.825509 0.564388i \(-0.809112\pi\)
−0.825509 + 0.564388i \(0.809112\pi\)
\(432\) 0 0
\(433\) −2372.81 −0.263349 −0.131674 0.991293i \(-0.542035\pi\)
−0.131674 + 0.991293i \(0.542035\pi\)
\(434\) 1181.89 3882.38i 0.130720 0.429401i
\(435\) 0 0
\(436\) 1831.95 + 1229.30i 0.201226 + 0.135030i
\(437\) −190.387 + 109.920i −0.0208408 + 0.0120325i
\(438\) 0 0
\(439\) 2509.56 + 1448.89i 0.272835 + 0.157522i 0.630175 0.776453i \(-0.282983\pi\)
−0.357340 + 0.933974i \(0.616316\pi\)
\(440\) 3955.53 + 4849.02i 0.428574 + 0.525382i
\(441\) 0 0
\(442\) 1659.54 + 7149.28i 0.178589 + 0.769359i
\(443\) −3932.06 + 6810.53i −0.421711 + 0.730425i −0.996107 0.0881526i \(-0.971904\pi\)
0.574396 + 0.818578i \(0.305237\pi\)
\(444\) 0 0
\(445\) 578.508 + 1002.00i 0.0616267 + 0.106741i
\(446\) 3733.55 3489.94i 0.396387 0.370523i
\(447\) 0 0
\(448\) 8215.90 9257.33i 0.866439 0.976267i
\(449\) 1335.91i 0.140413i −0.997532 0.0702064i \(-0.977634\pi\)
0.997532 0.0702064i \(-0.0223658\pi\)
\(450\) 0 0
\(451\) 8613.02i 0.899271i
\(452\) −5003.85 337.886i −0.520711 0.0351611i
\(453\) 0 0
\(454\) −2907.98 3110.97i −0.300613 0.321597i
\(455\) 3301.79 + 5718.87i 0.340198 + 0.589241i
\(456\) 0 0
\(457\) −8696.49 + 15062.8i −0.890164 + 1.54181i −0.0504849 + 0.998725i \(0.516077\pi\)
−0.839679 + 0.543084i \(0.817257\pi\)
\(458\) 4226.52 981.091i 0.431206 0.100095i
\(459\) 0 0
\(460\) −151.009 307.744i −0.0153061 0.0311927i
\(461\) 1933.14 + 1116.10i 0.195304 + 0.112759i 0.594463 0.804123i \(-0.297365\pi\)
−0.399159 + 0.916882i \(0.630698\pi\)
\(462\) 0 0
\(463\) 3435.96 1983.75i 0.344887 0.199121i −0.317544 0.948244i \(-0.602858\pi\)
0.662431 + 0.749123i \(0.269525\pi\)
\(464\) −2114.06 + 15582.5i −0.211514 + 1.55905i
\(465\) 0 0
\(466\) −3401.33 1035.45i −0.338120 0.102932i
\(467\) 8810.21 0.872993 0.436497 0.899706i \(-0.356219\pi\)
0.436497 + 0.899706i \(0.356219\pi\)
\(468\) 0 0
\(469\) 25253.4 2.48634
\(470\) 1413.38 + 430.266i 0.138711 + 0.0422270i
\(471\) 0 0
\(472\) −4792.23 1819.88i −0.467331 0.177472i
\(473\) 14476.3 8357.89i 1.40723 0.812466i
\(474\) 0 0
\(475\) −2306.68 1331.76i −0.222816 0.128643i
\(476\) −8978.70 + 4405.80i −0.864576 + 0.424243i
\(477\) 0 0
\(478\) 5052.89 1172.91i 0.483502 0.112234i
\(479\) 9734.00 16859.8i 0.928513 1.60823i 0.142702 0.989766i \(-0.454421\pi\)
0.785811 0.618466i \(-0.212246\pi\)
\(480\) 0 0
\(481\) 7409.42 + 12833.5i 0.702371 + 1.21654i
\(482\) −1385.90 1482.64i −0.130967 0.140109i
\(483\) 0 0
\(484\) −673.511 + 9974.23i −0.0632524 + 0.936723i
\(485\) 2551.05i 0.238840i
\(486\) 0 0
\(487\) 5226.26i 0.486293i 0.969990 + 0.243146i \(0.0781795\pi\)
−0.969990 + 0.243146i \(0.921820\pi\)
\(488\) −1257.69 7760.52i −0.116666 0.719882i
\(489\) 0 0
\(490\) −2715.57 + 2538.38i −0.250361 + 0.234025i
\(491\) −4793.56 8302.69i −0.440591 0.763127i 0.557142 0.830417i \(-0.311898\pi\)
−0.997733 + 0.0672904i \(0.978565\pi\)
\(492\) 0 0
\(493\) 6353.30 11004.2i 0.580402 1.00529i
\(494\) −896.303 3861.25i −0.0816327 0.351672i
\(495\) 0 0
\(496\) −3004.46 2324.29i −0.271984 0.210411i
\(497\) −5098.37 2943.55i −0.460147 0.265666i
\(498\) 0 0
\(499\) 2085.65 1204.15i 0.187108 0.108027i −0.403520 0.914971i \(-0.632213\pi\)
0.590628 + 0.806944i \(0.298880\pi\)
\(500\) 5347.69 7969.31i 0.478312 0.712797i
\(501\) 0 0
\(502\) 868.064 2851.49i 0.0771785 0.253523i
\(503\) 17192.1 1.52397 0.761985 0.647595i \(-0.224225\pi\)
0.761985 + 0.647595i \(0.224225\pi\)
\(504\) 0 0
\(505\) −9762.37 −0.860237
\(506\) 329.358 1081.91i 0.0289363 0.0950525i
\(507\) 0 0
\(508\) 318.014 473.915i 0.0277748 0.0413909i
\(509\) 2562.66 1479.55i 0.223159 0.128841i −0.384253 0.923228i \(-0.625541\pi\)
0.607412 + 0.794387i \(0.292208\pi\)
\(510\) 0 0
\(511\) −22918.0 13231.7i −1.98401 1.14547i
\(512\) −5370.32 10265.4i −0.463548 0.886072i
\(513\) 0 0
\(514\) −4420.27 19042.4i −0.379319 1.63410i
\(515\) 376.767 652.579i 0.0322375 0.0558370i
\(516\) 0 0
\(517\) 2437.08 + 4221.14i 0.207316 + 0.359083i
\(518\) −14752.3 + 13789.7i −1.25131 + 1.16966i
\(519\) 0 0
\(520\) 6101.36 988.798i 0.514543 0.0833878i
\(521\) 12490.4i 1.05032i 0.851004 + 0.525159i \(0.175994\pi\)
−0.851004 + 0.525159i \(0.824006\pi\)
\(522\) 0 0
\(523\) 13273.1i 1.10974i 0.831939 + 0.554868i \(0.187231\pi\)
−0.831939 + 0.554868i \(0.812769\pi\)
\(524\) 386.878 5729.40i 0.0322535 0.477652i
\(525\) 0 0
\(526\) −5119.24 5476.57i −0.424352 0.453973i
\(527\) 1534.70 + 2658.17i 0.126855 + 0.219719i
\(528\) 0 0
\(529\) 6052.52 10483.3i 0.497454 0.861616i
\(530\) 4511.03 1047.13i 0.369711 0.0858200i
\(531\) 0 0
\(532\) 4849.30 2379.53i 0.395195 0.193920i
\(533\) 7367.58 + 4253.68i 0.598734 + 0.345679i
\(534\) 0 0
\(535\) 3636.38 2099.47i 0.293859 0.169660i
\(536\) 8391.65 22097.5i 0.676239 1.78072i
\(537\) 0 0
\(538\) 6456.53 + 1965.53i 0.517400 + 0.157509i
\(539\) −12263.5 −0.980012
\(540\) 0 0
\(541\) −12385.8 −0.984302 −0.492151 0.870510i \(-0.663789\pi\)
−0.492151 + 0.870510i \(0.663789\pi\)
\(542\) 11601.1 + 3531.65i 0.919390 + 0.279885i
\(543\) 0 0
\(544\) 871.609 + 9320.67i 0.0686947 + 0.734596i
\(545\) −1300.17 + 750.656i −0.102190 + 0.0589992i
\(546\) 0 0
\(547\) −15941.6 9203.89i −1.24609 0.719433i −0.275766 0.961225i \(-0.588932\pi\)
−0.970328 + 0.241792i \(0.922265\pi\)
\(548\) 776.939 + 1583.34i 0.0605642 + 0.123425i
\(549\) 0 0
\(550\) 13347.2 3098.24i 1.03477 0.240199i
\(551\) −3431.35 + 5943.28i −0.265300 + 0.459514i
\(552\) 0 0
\(553\) −7406.78 12828.9i −0.569563 0.986512i
\(554\) −9335.03 9986.63i −0.715898 0.765869i
\(555\) 0 0
\(556\) −11195.5 755.975i −0.853944 0.0576627i
\(557\) 13864.9i 1.05472i 0.849643 + 0.527358i \(0.176817\pi\)
−0.849643 + 0.527358i \(0.823183\pi\)
\(558\) 0 0
\(559\) 16510.7i 1.24925i
\(560\) 3192.55 + 7794.35i 0.240910 + 0.588163i
\(561\) 0 0
\(562\) 3581.97 3348.25i 0.268854 0.251312i
\(563\) −7442.77 12891.3i −0.557150 0.965012i −0.997733 0.0672999i \(-0.978562\pi\)
0.440583 0.897712i \(1.64523\pi\)
\(564\) 0 0
\(565\) 1706.44 2955.65i 0.127063 0.220080i
\(566\) 2383.57 + 10268.4i 0.177012 + 0.762566i
\(567\) 0 0
\(568\) −4269.87 + 3483.09i −0.315422 + 0.257302i
\(569\) −5893.56 3402.65i −0.434219 0.250697i 0.266923 0.963718i \(-0.413993\pi\)
−0.701142 + 0.713021i \(0.747326\pi\)
\(570\) 0 0
\(571\) −7163.27 + 4135.72i −0.524998 + 0.303108i −0.738977 0.673731i \(-0.764691\pi\)
0.213979 + 0.976838i \(0.431357\pi\)
\(572\) 16932.7 + 11362.4i 1.23775 + 0.830572i
\(573\) 0 0
\(574\) −3376.22 + 11090.5i −0.245506 + 0.806461i
\(575\) −750.595 −0.0544382
\(576\) 0 0
\(577\) −12153.3 −0.876863 −0.438432 0.898765i \(-0.644466\pi\)
−0.438432 + 0.898765i \(0.644466\pi\)
\(578\) −1843.98 + 6057.27i −0.132698 + 0.435899i
\(579\) 0 0
\(580\) −8885.86 5962.73i −0.636147 0.426878i
\(581\) −11852.3 + 6842.92i −0.846327 + 0.488627i
\(582\) 0 0
\(583\) 13231.2 + 7639.04i 0.939932 + 0.542670i
\(584\) −19193.7 + 15657.0i −1.36000 + 1.10941i
\(585\) 0 0
\(586\) −4138.95 17830.5i −0.291772 1.25695i
\(587\) 7165.79 12411.5i 0.503856 0.872705i −0.496134 0.868246i \(-0.665247\pi\)
0.999990 0.00445871i \(-0.00141926\pi\)
\(588\) 0 0
\(589\) −828.874 1435.65i −0.0579850 0.100433i
\(590\) 2548.38 2382.10i 0.177822 0.166220i
\(591\) 0 0
\(592\) 7164.28 + 17491.0i 0.497382 + 1.21432i
\(593\) 17892.9i 1.23908i −0.784966 0.619539i \(-0.787319\pi\)
0.784966 0.619539i \(-0.212681\pi\)
\(594\) 0 0
\(595\) 6805.99i 0.468938i
\(596\) −11883.5 802.438i −0.816727 0.0551496i
\(597\) 0 0
\(598\) −762.804 816.049i −0.0521628 0.0558039i
\(599\) 5989.96 + 10374.9i 0.408586 + 0.707692i 0.994732 0.102514i \(-0.0326886\pi\)
−0.586145 + 0.810206i \(0.699355\pi\)
\(600\) 0 0
\(601\) −1473.48 + 2552.14i −0.100007 + 0.173218i −0.911687 0.410885i \(-0.865220\pi\)
0.811680 + 0.584102i \(0.198553\pi\)
\(602\) 21916.5 5087.43i 1.48381 0.344432i
\(603\) 0 0
\(604\) 6934.83 + 14132.7i 0.467176 + 0.952070i
\(605\) −5891.53 3401.48i −0.395909 0.228578i
\(606\) 0 0
\(607\) 22272.8 12859.2i 1.48933 0.859866i 0.489406 0.872056i \(-0.337214\pi\)
0.999926 + 0.0121903i \(0.00388040\pi\)
\(608\) −470.747 5034.00i −0.0314002 0.335782i
\(609\) 0 0
\(610\) 5118.06 + 1558.06i 0.339712 + 0.103417i
\(611\) 4814.36 0.318770
\(612\) 0 0
\(613\) −1851.43 −0.121988 −0.0609938 0.998138i \(-0.519427\pi\)
−0.0609938 + 0.998138i \(0.519427\pi\)
\(614\) 21264.7 + 6473.49i 1.39768 + 0.425487i
\(615\) 0 0
\(616\) −9865.20 + 25977.7i −0.645260 + 1.69914i
\(617\) −17363.4 + 10024.8i −1.13294 + 0.654103i −0.944673 0.328015i \(-0.893621\pi\)
−0.188267 + 0.982118i \(0.560287\pi\)
\(618\) 0 0
\(619\) 19210.5 + 11091.2i 1.24739 + 0.720183i 0.970589 0.240743i \(-0.0773911\pi\)
0.276805 + 0.960926i \(0.410724\pi\)
\(620\) 2320.61 1138.71i 0.150319 0.0737609i
\(621\) 0 0
\(622\) 20636.7 4790.34i 1.33031 0.308802i
\(623\) −2568.90 + 4449.46i −0.165202 + 0.286138i
\(624\) 0 0
\(625\) −2694.67 4667.31i −0.172459 0.298708i
\(626\) 16627.4 + 17788.1i 1.06161 + 1.13571i
\(627\) 0 0
\(628\) 608.094 9005.44i 0.0386395 0.572223i
\(629\) 15273.1i 0.968166i
\(630\) 0 0
\(631\) 28148.1i 1.77584i 0.459994 + 0.887922i \(0.347851\pi\)
−0.459994 + 0.887922i \(0.652149\pi\)
\(632\) −13687.0 + 2218.14i −0.861452 + 0.139609i
\(633\) 0 0
\(634\) −11226.8 + 10494.3i −0.703269 + 0.657382i
\(635\) 194.191 + 336.348i 0.0121358 + 0.0210198i
\(636\) 0 0
\(637\) −6056.53 + 10490.2i −0.376716 + 0.652492i
\(638\) −7982.77 34389.6i −0.495362 2.13401i
\(639\) 0 0
\(640\) 7881.16 203.534i 0.486766 0.0125709i
\(641\) −6980.56 4030.23i −0.430134 0.248338i 0.269270 0.963065i \(-0.413218\pi\)
−0.699404 + 0.714727i \(0.746551\pi\)
\(642\) 0 0
\(643\) −666.166 + 384.611i −0.0408570 + 0.0235888i −0.520289 0.853990i \(-0.674176\pi\)
0.479432 + 0.877579i \(0.340843\pi\)
\(644\) 848.193 1264.00i 0.0518998 0.0773428i
\(645\) 0 0
\(646\) −1189.79 + 3908.33i −0.0724639 + 0.238036i
\(647\) −25155.2 −1.52852 −0.764259 0.644909i \(-0.776895\pi\)
−0.764259 + 0.644909i \(0.776895\pi\)
\(648\) 0 0
\(649\) 11508.5 0.696067
\(650\) 3941.47 12947.3i 0.237842 0.781283i
\(651\) 0 0
\(652\) −8648.13 + 12887.7i −0.519458 + 0.774114i
\(653\) −17852.0 + 10306.9i −1.06984 + 0.617671i −0.928137 0.372238i \(-0.878590\pi\)
−0.141701 + 0.989910i \(0.545257\pi\)
\(654\) 0 0
\(655\) 3384.21 + 1953.88i 0.201881 + 0.116556i
\(656\) 8582.62 + 6639.64i 0.510815 + 0.395175i
\(657\) 0 0
\(658\) 1483.44 + 6390.65i 0.0878886 + 0.378622i
\(659\) −12082.8 + 20928.0i −0.714231 + 1.23708i 0.249024 + 0.968497i \(0.419890\pi\)
−0.963255 + 0.268587i \(0.913443\pi\)
\(660\) 0 0
\(661\) −9976.53 17279.9i −0.587053 1.01681i −0.994616 0.103629i \(-0.966955\pi\)
0.407563 0.913177i \(-0.366379\pi\)
\(662\) −3262.06 + 3049.22i −0.191516 + 0.179020i
\(663\) 0 0
\(664\) 2049.27 + 12645.0i 0.119770 + 0.739038i
\(665\) 3675.84i 0.214351i
\(666\) 0 0
\(667\) 1933.95i 0.112268i
\(668\) −1339.37 + 19835.2i −0.0775777 + 1.14887i
\(669\) 0 0
\(670\) 10984.1 + 11750.9i 0.633365 + 0.677575i
\(671\) 8825.05 + 15285.4i 0.507731 + 0.879416i
\(672\) 0 0
\(673\) 3449.60 5974.88i 0.197581 0.342221i −0.750162 0.661254i \(-0.770025\pi\)
0.947744 + 0.319033i \(0.103358\pi\)
\(674\) 18737.2 4349.43i 1.07082 0.248566i
\(675\) 0 0
\(676\) 2303.16 1130.15i 0.131040 0.0643007i
\(677\) 7812.18 + 4510.37i 0.443496 + 0.256052i 0.705079 0.709128i \(-0.250911\pi\)
−0.261584 + 0.965181i \(0.584245\pi\)
\(678\) 0 0
\(679\) 9810.44 5664.06i 0.554477 0.320128i
\(680\) −5955.44 2261.61i −0.335854 0.127543i
\(681\) 0 0
\(682\) 8158.33 + 2483.59i 0.458062 + 0.139445i
\(683\) 7388.19 0.413911 0.206956 0.978350i \(-0.433644\pi\)
0.206956 + 0.978350i \(0.433644\pi\)
\(684\) 0 0
\(685\) −1200.20 −0.0669448
\(686\) 6645.30 + 2022.99i 0.369853 + 0.112592i
\(687\) 0 0
\(688\) 2831.16 20868.2i 0.156885 1.15638i
\(689\) 13068.9 7545.32i 0.722620 0.417205i
\(690\) 0 0
\(691\) −25972.9 14995.5i −1.42989 0.825549i −0.432781 0.901499i \(-0.642468\pi\)
−0.997112 + 0.0759500i \(0.975801\pi\)
\(692\) −10143.5 20671.7i −0.557224 1.13558i
\(693\) 0 0
\(694\) −34319.0 + 7966.38i −1.87713 + 0.435734i
\(695\) 3817.95 6612.88i 0.208378 0.360922i
\(696\) 0 0
\(697\) −4384.06 7593.41i −0.238247 0.412656i
\(698\) −3518.06 3763.63i −0.190775 0.204091i
\(699\) 0 0
\(700\) 18400.9 + 1242.52i 0.993554 + 0.0670899i
\(701\) 23559.3i 1.26936i −0.772774 0.634681i \(-0.781131\pi\)
0.772774 0.634681i \(-0.218869\pi\)
\(702\) 0 0
\(703\) 8248.82i 0.442547i
\(704\) 19453.1 + 17264.7i 1.04143 + 0.924272i
\(705\) 0 0
\(706\) 14362.1 13425.0i 0.765618 0.715663i
\(707\) −21675.2 37542.6i −1.15301 1.99708i
\(708\) 0 0
\(709\) −6114.96 + 10591.4i −0.323910 + 0.561028i −0.981291 0.192530i \(-0.938331\pi\)
0.657381 + 0.753558i \(0.271664\pi\)
\(710\) −847.887 3652.68i −0.0448178 0.193074i
\(711\) 0 0
\(712\) 3039.78 + 3726.41i 0.160001 + 0.196142i
\(713\) −404.574 233.581i −0.0212502 0.0122688i
\(714\) 0 0
\(715\) −12017.5 + 6938.30i −0.628571 + 0.362906i
\(716\) −19701.6 13220.5i −1.02833 0.690046i
\(717\) 0 0
\(718\) −262.555 + 862.464i −0.0136469 + 0.0448285i
\(719\) 37718.6 1.95642 0.978211 0.207613i \(-0.0665694\pi\)
0.978211 + 0.207613i \(0.0665694\pi\)
\(720\) 0 0
\(721\) 3346.11 0.172837
\(722\) −5007.29 + 16448.4i −0.258105 + 0.847848i
\(723\) 0 0
\(724\) −8307.38 5574.55i −0.426438 0.286156i
\(725\) −20292.0 + 11715.6i −1.03949 + 0.600147i
\(726\) 0 0
\(727\) 7555.48 + 4362.16i 0.385443 + 0.222536i 0.680184 0.733041i \(-0.261900\pi\)
−0.294741 + 0.955577i \(0.595233\pi\)
\(728\) 17349.3 + 21268.2i 0.883252 + 1.08276i
\(729\) 0 0
\(730\) −3811.38 16419.4i −0.193241 0.832476i
\(731\) −8508.39 + 14737.0i −0.430498 + 0.745645i
\(732\) 0 0
\(733\) 7960.97 + 13788.8i 0.401153 + 0.694817i 0.993865 0.110597i \(-0.0352762\pi\)
−0.592712 + 0.805414i \(0.701943\pi\)
\(734\) −12944.2 + 12099.6i −0.650923 + 0.608452i
\(735\) 0 0
\(736\) −824.189 1162.22i −0.0412772 0.0582065i
\(737\) 53066.9i 2.65230i
\(738\) 0 0
\(739\) 21026.0i 1.04662i −0.852141 0.523312i \(-0.824696\pi\)
0.852141 0.523312i \(-0.175304\pi\)
\(740\) −12833.2 866.565i −0.637511 0.0430480i
\(741\) 0 0
\(742\) 14042.7 + 15022.9i 0.694774 + 0.743271i
\(743\) 5813.11 + 10068.6i 0.287029 + 0.497148i 0.973099 0.230387i \(-0.0739992\pi\)
−0.686071 + 0.727535i \(0.740666\pi\)
\(744\) 0 0
\(745\) 4052.60 7019.32i 0.199297 0.345192i
\(746\) −33426.8 + 7759.27i −1.64054 + 0.380814i
\(747\) 0 0
\(748\) −9258.24 18867.6i −0.452560 0.922284i
\(749\) 16147.6 + 9322.82i 0.787744 + 0.454804i
\(750\) 0 0
\(751\) 6096.06 3519.56i 0.296203 0.171013i −0.344533 0.938774i \(-0.611963\pi\)
0.640736 + 0.767761i \(0.278629\pi\)
\(752\) 6084.95 + 825.539i 0.295074 + 0.0400323i
\(753\) 0 0
\(754\) −33359.3 10155.4i −1.61124 0.490500i
\(755\) −10712.8 −0.516395
\(756\) 0 0
\(757\) −28354.3 −1.36137 −0.680685 0.732577i \(-0.738318\pi\)
−0.680685 + 0.732577i \(0.738318\pi\)
\(758\) −5218.77 1588.72i −0.250072 0.0761279i
\(759\) 0 0
\(760\) 3216.47 + 1221.47i 0.153518 + 0.0582994i
\(761\) 20274.5 11705.5i 0.965771 0.557588i 0.0678265 0.997697i \(-0.478394\pi\)
0.897944 + 0.440109i \(0.145060\pi\)
\(762\) 0 0
\(763\) −5773.51 3333.34i −0.273939 0.158158i
\(764\) −5569.79 + 2733.07i −0.263754 + 0.129423i
\(765\) 0 0
\(766\) 16392.9 3805.24i 0.773237 0.179490i
\(767\) 5683.65 9844.37i 0.267568 0.463441i
\(768\) 0 0
\(769\) 12632.8 + 21880.6i 0.592392 + 1.02605i 0.993909 + 0.110202i \(0.0351498\pi\)
−0.401517 + 0.915852i \(0.631517\pi\)
\(770\) −12912.9 13814.3i −0.604350 0.646535i
\(771\) 0 0
\(772\) 2356.08 34891.9i 0.109841 1.62667i
\(773\) 31081.3i 1.44621i −0.690740 0.723103i \(-0.742715\pi\)
0.690740 0.723103i \(-0.257285\pi\)
\(774\) 0 0
\(775\) 5660.02i 0.262340i
\(776\) −1696.24 10466.6i −0.0784682 0.484186i
\(777\) 0 0
\(778\) 4827.00 4512.05i 0.222438 0.207924i
\(779\) 2367.78 + 4101.12i 0.108902 + 0.188624i
\(780\) 0 0